How do you find the roots for #4x^4-26x^3+50x^2-52x+84=0#?

1 Answer
Feb 18, 2015

The easiest way to find the roots (also known as zeroes and factors) of this equation would be to plug it in your graphing calculator, and find all 4 of them using 2ND#->#CALC#->#ZERO and find your roots (this video will show you exactly how to do that).

Now if your four zeroes are NOT all rational/real numbers, then you'd need to find one of your zeroes, and then use synthetic division till you got a quadratic, and then use factoring/the quadratic formula.

Here are videos for all the above ideas:

Synthetic Division


Quadratic Formula

In your case, you have two real zeroes, and two unreal. Therefore, you'll need to condense this down to a quadratic using synthetic division, and then use quadratic formula.

The real zeroes are 3, 3.5, and the unreal zeroes are #+-isqrt(2)#. I'll leave the work for you to solve.

Hope that helped :)